## A Treatise on Plane Trigonometry |

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2ikir absolutely convergent algebraical angles OA angular points approximate becomes infinite calculate centre circular functions circular measure circum-circle coefficients complex quantities continuous function convergent series corresponding cos2 cos3 cosec cosh cosine cotangent deduced difference distance equal escribed circles expand expression factors fraction geometrical given hence infinite series inscribed integer last Article length less than unity lies limiting value logarithms magnitude modulus multiple nine-point circle nth root pedal triangle perpendicular places of decimals plane positive integer positive or negative powers principal value projection Prove quadrilateral radii ratio real quantity regular polygon respectively right angles roots series is convergent shew shewn similar manner sin2 sin3 sine sines and cosines sinh straight line subtends suppose tables tan2 tangent tanh theorem triangle ABC Trigonometrical value of Log zero

### Popular passages

Page 285 - Show that the perimeter p of a regular polygon of n sides inscribed in a circle of radius R...

Page 182 - The angular elevation of a tower at a place A due south of it is 30° ; and at a place B due west of A, and at a distance...

Page 192 - The three perpendiculars from the vertices of a triangle to the opposite sides (produced if necessary) are called the altitudes...

Page v - These definitions appear to the author to be " those from which the fundamental properties of the functions may be most easily deduced in such a way that the proofs may be quite general, in that they apply to angles of all magnitudes. It will be seen that this method...

Page 237 - N turns is in the foim of a regular polygon of n sides inscribed in a circle of radius R meters.

Page 139 - We have, then, that the sine of an angle is equal to the cosine of its complement, and conversely.

Page 216 - Pro.ve that the equilateral triangle described on the hypotenuse of a right.angled triangle is equal to the sum of the equilateral triangles described on the sides containing the right angle.

Page 182 - ... from another station due west of the former and distant a mile from it is 45° : find the height of the balloon. Ans. 6468 feet. 69. Find the height of a hill, the angle of elevation at its foot being 60°, and at a point 500 yards from the foot along a horizontal plane 30°. Ans. 250V3 yards. 70. A tower 51 feet high has a mark at a height of 25 feet from the ground : find at what distance from the foot the two parts subtend equal angles. Ans. 25V51 feet 71. The angles of a triangle are as 1:2:3,...

Page 40 - The sum of the sines of two angles is equal to twice the product of the sine of half the sum of the given angles into the cosine of half the difference of the given angles.

Page 153 - Law of Sines — In any triangle, the sides are proportional to the sines of the opposite angles. That is, sin A = sin B...